Energy Level Repulsion Research Articles

Anderson Localization in the Subwavelength Regime

In this paper, we use recent breakthroughs in the study of coupled subwavelength resonator systems to reveal new insight into the mechanisms responsible for the fundamental features of Anderson localization. The occurrence of strong localization in random media has proved difficult to understand, particularly in physically derived multi-dimensional models and systems with long-range interactions. We show here that the scattering of time-harmonic waves by high-contrast resonators with randomly chosen material parameters reproduces the characteristic features of Anderson localization. In particular, we show that the hybridization of subwavelength resonant modes is responsible for both the repulsion of energy levels as well as the widely observed phase transition, at which point eigenmode symmetries swap and very strong localization is possible. We derive results from first principles, using asymptotic expansions in terms of the material contrast parameter and obtain a characterization of the localized modes in terms of generalized capacitance matrices. This model captures the long-range interactions of the wave-scattering system and provides a concise framework to explain the exotic phenomena that are observed.

Effects of autocorrelated disorder on the dynamics in the vicinity of the many-body localization transition

The presence of frozen uncorrelated random on-site potential in interacting quantum systems can induce a transition from an ergodic phase to a localized one, the so-called many-body localization. Here we numerically study the effects of autocorrelated disorder on the static and dynamical properties of a one-dimensional many-body quantum system which exhibits many-body localization. Specifically, by means of some standard measures of energy level repulsion and localization of energy eigenstates, we show that a strong degree of correlations between the on-site potentials in the one-dimensional spin-1/2 Heisenberg model leads to suppression of the many-body localization phase, while level repulsion is mitigated for small disorder strengths, although energy eigenstates remain well extended. Our findings are also remarkably manifested in the time domain, on which we put the main emphasis, as shown by the time evolution of experimentally relevant observables, like the return probability and the spin autocorrelation function.

Non-ergodic delocalized phase with Poisson level statistics

Motivated by the many-body localization (MBL) phase in generic interacting disordered quantum systems, we develop a model simulating the same eigenstate structure like in MBL, but in the random-matrix setting. Demonstrating the absence of energy level repulsion (Poisson statistics), this model carries non-ergodic eigenstates, delocalized over the extensive number of configurations in the Hilbert space. On the above example, we formulate general conditions to a single-particle and random-matrix models in order to carry such states, based on the transparent generalization of the Anderson localization of single-particle states and multiple resonances.

The magnetic proximity effect at the MoS2/CrI3 interface

The vicinity to a two-dimensional magnetic material provides a simple and effective way to break the valley degeneracy of transition-metal dichalcogenides because of the magnetic proximity effect. Based on first-principles calculations, we study the band structure of a MoS2/CrI3 van der Waals heterostructure and its manipulation by vertical electric fields. A huge valley splitting of about 19.60 meV, equivalent to an external magnetic fields of about 89.0 T can be generated by an electric field of 0.115 V Å−1. The electric field causes discontinuous changes in the valley splitting. The electric field drives the bands of MoS2 across those of CrI3. At the critical electric fields, the interlayer orbital hybridization leads to the energy level repulsion and an abrupt exchange of the band index. We also study the effect of interlayer distance on the valley splitting and observe a more significant electric field modulation. This work deepens our understanding on the interfacial magnetic proximity effect as a result of the orbital hybridization across the van der Waals gap.

Shannon entropy as a predictor of avoided crossing in confined atoms

AbstractAvoided crossing is one of the unique spectroscopic features of a confined atomic system. Shannon information entropy of the ground state and some of the excited states of confined H atom as a predictor of avoided crossing is studied in this work. This is accomplished by varying the strength of the confinement and examining structure properties like ionization energy and Shannon information entropy. Along with the energy level repulsion at the avoided crossing, Shannon information entropy is also exchanged between the involved states. This work also addresses a question: In addition to that regarding localization, what other property of the system can be extracted from Shannon entropy? Insightful connection is discovered between Shannon entropy and the average value of confinement potential, Coulomb potential, and kinetic energy.

Entropic uncertainty as a predictor of avoided crossing for confined system

SynopsisAvoided Crossings are one of the unique spectroscopic features of confined atomic system. Shannon’s information entropy as a predictor of these phenomena by varying the perturbation (confinement strength) on ground state and some of excited states of H atom is studied in this work. In addition to the energy level repulsion at avoided crossing, it is observed that Shannon’s entropy also assures the exchange of information of involved states, and also validates entopic uncertainty.

Level repulsion and dynamics in the finite one-dimensional Anderson model

This work shows that dynamical features typical of full random matrices can be observed also in the simple finite one-dimensional (1D) noninteracting Anderson model with nearest-neighbor couplings. In the thermodynamic limit, all eigenstates of this model are exponentially localized in configuration space for any infinitesimal on-site disorder strength W. But this is not the case when the model is finite and the localization length is larger than the system size L, which is a picture that can be experimentally investigated. We analyze the degree of energy-level repulsion, the structure of the eigenstates, and the time evolution of the finite 1D Anderson model as a function of the parameter ξ∝(W^{2}L)^{-1}. As ξ increases, all energy-level statistics typical of random matrix theory are observed. The statistics are reflected in the corresponding eigenstates and also in the dynamics. We show that the probability in time to find a particle initially placed on the first site of an open chain decays as fast as in full random matrices and much faster than when the particle is initially placed far from the edges. We also see that at long times, the presence of energy-level repulsion manifests in the form of the correlation hole. In addition, our results demonstrate that the hole is not exclusive to random matrix statistics, but emerges also for W=0, when it is in fact deeper.

Energy-level repulsion by spin-orbit coupling in two-dimensional Rydberg excitons

We study the effects of Rashba spin-orbit coupling on two-dimensional Rydberg exciton systems. Using analytical and numerical arguments we demonstrate that this coupling considerably modifies the wave functions and leads to a level repulsion that results in a deviation from the Poissonian statistics of the adjacent level distance distribution. This signifies the crossover to non-integrability of the system and hints on the possibility of quantum chaos emerging. Such a behavior strongly differs from the classical realization, where spin-orbit coupling produces highly entangled, chaotic electron trajectories in an exciton. We also calculate the oscillator strengths and show that randomization appears in the transitions between states with different total momenta.

Sonic metamaterials: Reflection on the role of topology on dispersion surface morphology

Investigating dispersion surface morphology of sonic metamaterials is crucial in providing information on related phenomena as inertial coupling, acoustic transparency, polarisation, and absorption. In the present study, we look into frequency surface morphology of two-dimensional (2D) metamaterials of K3,3 and K6 topologies. The elastic structures under consideration consist of the same substratum lattice points and form a pair of sublattices with hexagonal symmetry. We show that, through introducing universal localised mass-in-mass phononic microstructures at lattice points, six single optical frequency-surfaces can be formed with required properties including negative group velocity. Splitting the frequency-surfaces is based on the classical analog of the quantum phenomenon of ‘energy-level repulsion’, which can be achieved only through internal anisotropy of the nodes and allows us to obtain different frequency band gaps.

Quasiparticle-continuum level repulsion in a quantum magnet

A neutron scattering study of the quantum magnet BiCu2PO6 demonstrates a phenomenon known as energy-level repulsion, which occurs between a long-lived quasiparticle state and a many-particle continuum. When the energy eigenvalues of two coupled quantum states approach each other in a certain parameter space, their energy levels repel each other and level crossing is avoided1. Such level repulsion, or avoided level crossing, is commonly used to describe the dispersion relation of quasiparticles in solids2. However, little is known about the level repulsion when more than two quasiparticles are present; for example, in a strongly interacting quantum system where a quasiparticle can spontaneously decay into a many-particle continuum3,4,5. Here we show that even in this case level repulsion exists between a long-lived quasiparticle state and a continuum. In our fine-resolution neutron spectroscopy study of magnetic quasiparticles in the frustrated quantum magnet BiCu2PO6, we observe a renormalization of the quasiparticle dispersion relation due to the presence of the continuum of multi-quasiparticle states.

Random-matrix theory of Majorana fermions and topological superconductors

I. Introduction (What is new in RMT, Superconducting quasiparticles, Experimental platforms) II. Topological superconductivity (Kitaev chain, Majorana operators, Majorana zero-modes, Phase transition beyond mean-field) III. Fundamental symmetries (Particle-hole symmetry, Majorana representation, Time-reversal and chiral symmetry) IV. Hamiltonian ensembles (The ten-fold way, Midgap spectral peak, Energy level repulsion) V. Scattering matrix ensembles (Fundamental symmetries, Chaotic scattering, Circular ensembles, Topological quantum numbers) VI. Electrical conduction (Majorana nanowire, Counting Majorana zero-modes, Conductance distribution, Weak antilocalization, Andreev resonances, Shot noise of Majorana edge modes) VII. Thermal conduction (Topological phase transitions, Super-universality, Heat transport by Majorana edge modes, Thermopower and time-delay matrix, Andreev billiard with chiral symmetry) VIII. Josephson junctions (Fermion parity switches, 4{\pi}-periodic Josephson effect, Discrete vortices) IX. Conclusion

Photodetachment spectroscopy of fluorenone radical anions microsolvated with methanol: rationalizing the anomalous solvatochromic behavior due to hydrogen bonding.

The attribution of the extraordinary blue shift for the intramolecular charge-transfer absorption band of fluorenone radical anion solvated in protic media was investigated by means of photodetachment spectroscopy of the gas-phase anions microsolvated with methanol, in conjunction with quantum chemical calculations based on density functional theory. Sequential shifts of the vertical detachment energy as a function of the cluster size are consistent with theoretical predictions, where up to two methanol molecules can directly attach to the carbonyl group. In the photodetachment excitation spectra as alternatives to the photoabsorption spectra, with increasing cluster size, a new absorption band grows in the higher-energy region, which coincides with the blue-shifted band in protic media. Spectral simulations using time-dependent density functional theory with the CAM-B3LYP functional reproduced the feature of the phenomenon. Analyses on the electronic configuration elucidated that the extraordinarily blue shifts originate from energy-level repulsion due to solvation-induced resonant coupling with another electronic state. The orbital transition for the counterpart state corresponds to the first absorption band of the neutral fluorenone molecule, which has small oscillator strength from the ground state. It was found that correction of long-range electron exchange correlation is important for the spectral simulation involving the electronic-state coupling.

Photoinduced cation interstitial diffusion in II–VI semiconductors

The electronic structure, stability, and chemical trend of cation interstitials in II--VI semiconductors are studied through ab initio methods. We find that interstitials in the neutral charge state are more stable in the tetrahedral interstitial site near the cation $({T}_{C})$, whereas in the $(2+)$ charge state, they are more stable near the anion $({T}_{A})$. This bistability is explained through the Coulomb coupling and energy-level repulsion in the two different interstitial sites. We show that the diffusion energy barrier changes when the defect charge state changes. We suggest that if electrons or holes are taken from the defect level by light, changing its charge state, the interstitial atom will be able to diffuse almost spontaneously due to a reduced diffusion barrier. These results can help unravel the nature of the recently observed photoinduced migration of interstitials in II--VI semiconductors.

Characterization of atomic avoided crossings by means of Fisher?s information

Atomic avoided crossings in strong magnetic and electric fields are usually identified by the energy level repulsion and by the sharp extremal value of the Shannon's entropy of the two involved states. In this work the proposal of a new information-theoretic parameter, the continuous Fisher information, for the prediction and characterization of these nonlinear phenomena is done. For just around the irregular region it is found that Fisher's informations of the two states cross over and show that the states exchange their informational character. Moreover, the state Fisher information sum keeps constant through the avoided crossing. This is illustrated for some hydrogenic excited states in strong magnetic fields as well as in parallel magnetic and electric fields.

Shannon entropy as an indicator of atomic avoided crossings in strong parallel magnetic and electric fields.

Avoided crossings are the most distinctive atomic spectroscopic features in the presence of magnetic and electric fields. We point out the role of Shannon's information entropy as an indicator or predictor of these phenomena by studying the dynamics of some excited states of hydrogen in the presence of parallel magnetic and electric fields. Moreover, in addition to the well-known energy level repulsion, it is found that Shannon's entropy manifests the informational exchange of the involved states as the magnetic field strength is varied across the narrow region where an avoided crossing occurs.

Measuring the energy level repulsion in quantum dots

Energy level repulsion is one of the remnants of classical chaos in quantum mechanics. Measurements of the distribution of nearest neighbor spacings in quantum dots reveal, in contrast to other classically chaotic systems, deviations from the predictions made by random matrix theory. Here, we survey possible contributions to these deviations from experimental peculiarities present in measurements on quantum dots, and discuss the methods to eliminate or reduce such distortions.

Diamagnetic informational exchange in hydrogenic avoided crossings

The irregular behavior of the hydrogen atom in the presence of strong magnetic fields is examined by means of the ionization energy and the Shannon information entropy of the excited states involved in some high-lying avoided crossings. In addition to the energy level repulsion, which is known to occur for a certain field strength in going through a chaotic region of this type, it is found that the two states: (i) show up maximal entropies for just around this critical field and (ii) exchange their informational character in that region.

Quantum mechanical repulsion of exciton levels in a disordered quantum well evidenced by near-field spectroscopy

Near-field photoluminescence spectra of a single quantum well dominated by emission from localized excitons are subjected to a statistical analysis of the two-energy autocorrelation function. This analysis is compared to a theoretical model of the exciton center-of-mass motion in a two-dimensional spatially correlated disordered potential. The spatial and energetic parameters of the disorder potential underlying the excitonic motion are extracted and clear signatures of quantum-mechanical energy level repulsion are revealed.

Parametric dynamics of level spacings in quantum chaos

We identify parametric (radial) Bessel–Ornstein–Uhlenbeck stochastic processes as primitive dynamical models of energy level repulsion in irregular quantum systems. Familiar GOE, GUE, GSE and non-Hermitian Ginibre-type (Wigner surmise) level spacing distributions arise as special cases in that formalism, as densities of asymptotic invariant (equilibrium) probability measures.

Quantum mechanical repulsion of exciton levels in a disordered quantum well.

Spatially resolved photoluminescence spectra of a single quantum well are recorded by near-field spectroscopy. A set of over four hundred spectra displaying sharp emission lines from localized excitons is subject to a statistical analysis of the two-energy autocorrelation function. An accurate comparison with a quantum theory of the exciton center-of-mass motion in a two-dimensional spatially correlated disordered potential reveals clear signatures of quantum mechanical energy level repulsion, giving the spatial and energetic correlations of excitons in disordered quantum systems.